Journal of Mathematical Psychology volume 49, issue 1, P87-113 2005 DOI: 10.1016/j.jmp.2004.08.002 View full text
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Abstract: An overview of the role of dual geometries in statistics is given, beginning with the classical result on the relative Fisher information loss of a statistic for summarizing a curved exponential family. Exponential families are an important class of parametric statistical models that include many important models for applications such as the Normal, binomial, and Poisson distributions, and that have desirable theoretical properties such as parameter estimates that are sufficient. Curved exponential families a…

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